Godwin: A couple of things to keep in mind--
to go east to west through VT you will have to go over the Green Mountains through one of the "gaps." Don't let the name fool you--there's a lot of elevation gain there. If you're meaning to connect with 74 on the NY side, you'll need to go over either the Brandon Gap or the Middlebury Gap. Brandon is easier, but longer, and will add miles; Middlebury has a steady 3 mile pitch coming from the Hancock side, but once you get to the top it's almost all downhill to the Ticonderoga cable ferry in Shoreham, which will get you across Lake Champlain to 74 in a jiffy and is really fun.
Meanwhile, on the NY side, RT 74 has an extremely long and arduous climb coming out of Ticonderoga called Chilson Hill. All amenities are at the bottom of the hill, and it will be quite a while before you see another store or a place to get water. (There may be a general store in Paradox, but it may be out of business. There's a summer camp where you may be able to refill your water, near there, right on the road.) 74 can be a tricky road past Paradox: it gets narrow and there is no shoulder and it's twisty and you have to watch out for trucks and campers and of course deer. When there's little traffic on it, it's quite nice.
At the end of 74, to get to 28, you're going to have to ride on Rt9. 9 is a two-lane but popular N-S road. Cyclists ride it, for sure, but you have to do so with caution because, like 74, it is narrow. A couple of weeks ago a cyclist coming down a hill (in the opposite direction from you) was hit by a car pulling out of a side road. The car didn't see the cyclist till they collided, in part because he wasn't anticipating him.
You will have no trouble finding provisions or a place to stay on Rt. 9.
Since you're trying to get to Rt. 28, you might want to turn off Rt 9 in Pottersville and head up towards Minerva and Olmsteadville. There's some climbing (but that's true all over the Adirondacks), but you'll be on back roads with not a lot of traffic. You can get provisions in Pottersville, and Minerva (they have one store each). Instead of ending up on 28, you'll be on 28 N, which you'll take through Newcomb and then over to Blue Mountain Lake, which is on Rt. 30. Rt. 30 goes to Old Forge.
Alternatively, you can go through Pottersville, turn left on Igerna Road, and follow the signs to North Creek, where you can pick up Rt. 28 and head up it more directly to Blue. Rt. 28 is a big climb, but it's a great biking road. There are places to stay in and around N.Creek, Indian Lake and Blue. There's a bike shop in N.Creek. There's also one in Middlebury. There's a Walmart (ugh) in Ticonderoga.
You may be able to get good maps for the NY part from the NYState Department of Environmental Conservation or from the tourist board. I think someone publishes a map of bike routes in VT. (Not sure who.)
Just make sure you've got your climbing legs on. Good luck! It's gorgeous.